# Centre of mass of solid cone

Tags:
1. Mar 29, 2015

1. The problem statement, all variables and given/known data

Find the centre of mass of solid cone.
2. Relevant equations

$$y_{cm}=\frac{1}{M}\int_0^Hydm$$
3. The attempt at a solution
First I took thin disks. I got the answer when I assumed its thickness to be dy but then dysecθ would be more accurate if half angle of cone is θ since dysecθ gives the length of the slanted part, while dy would give a cylinder.

#### Attached Files:

• ###### 20150329_111211-1.jpg
File size:
29.3 KB
Views:
540
2. Mar 29, 2015

### ehild

But the volume of a truncated cone is (h pi/3 )(r12+r1r2+r22) where r1 and r2 are the radii of the base plates and h is the height. In case of the volume element, r1≈r2=r and h=dy, so the volume element is that of a disk with radius r and height dy.

Also, you have to use density times Ady instead of dm in the integral.

Last edited: Mar 29, 2015
3. Mar 29, 2015